English: in this thesis, we address the problem of learning a face manifold model from an input data, consisting of 2D face images such that the input images can be approximated well using the learned manifold. We compute the face manifold in terms of a depth pattern and a texture pattern, which define a face model together. Given the depth pattern and the texture pattern of the individual face, the images of this face from different viewpoints can be rendered by changing the camera parameters. Along with the depth and texture patterns, we compute a parameter vector for each input image, which gives the registration of the image with respect to the computed manifold. Then, the approximation of each input image is given by its projection on the manifold, i.e., the image rendered from the model with the parameter vector corresponding to the image. In the computation of the depth pattern and the texture pattern, we represent both patterns in terms of some elementary functions called "atoms". We have chosen to use parametric and smooth atoms, i.e., atoms derived from smooth generating functions, in the construction of the manifold. The usage of smooth and parametric atoms in the model results in a more regular manifold, which facilitates the registration of face images with respect to the manifold, and the ease of efficient storage of the model information.